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The short answer is that the Edman degradation is a multi-step process. The Wikipedia page has a decent picture of the mechanism. In practice, the peptide is reacted with phenylisothiocyanate (PTH) under mildly basic conditions to give a thiourea, which is stable. The excess PTH is separated from the thiourea intermediate. The thiourea is then treated with ...

Th reason for this is that for the third base of the tRNA non-Watson-Crick pairing is allowed. This phenomenon is called "Wobble base pairing". See the figure (from here) for illustration (from here):
If you have a look at the codon table for amino acids, than the variation in the code for one amino acid mostly happens on the third position (from here):
...

Watson-Crick base pairing can be violated by wobble base pairing.
The 5' of the anticodon has more freedom in binding, that is why, for many amino acids, the last part of the codon has more possible characters.

To put it shortly:
Proteins have properties that individual amino acids that make up the protein does not have.
Similarly the individual amino acids have properties that the protein does not have.
This is analogous to elements vs compounds.
The site referenced below quotes 3 experiments done to examine this phenomena.
All experiments compared ...